Some rao-guttman relationships

An examination of the determinantal equation associated with Rao's canonical factors suggests that Guttman's best lower bound for the number of common factors corresponds to the number of positive canonical correlations when squared multiple correlations are used as the initial estimates of communality. When these initial communality estimates are used, solving Rao's determinantal equation (at the first stage) permits expressing several matrices as functions of factors that differ only in the scale of their columns; these matrices include the correlation matrix with units in the diagonal, the correlation matrix with squared multiple correlations as communality estimates, Guttman's image covariance matrix, and Guttman's anti-image covariance matrix. Further, the factor scores associated with these factors can be shown to be either identical or simply related by a scale change. Implications for practice are discussed, and a computing scheme which would lead to an exhaustive analysis of the data with several optional outputs is outlined.     

Beyond the group mind: a quantitative review of the interindividual-intergroup discontinuity effect

This quantitative review of 130 comparisons of interindividual and intergroup interactions in the context of mixed-motive situations reveals that intergroup interactions are generally more competitive than interindividual interactions. The authors identify 4 moderators of this interindividual-intergroup discontinuity effect, each based on the theoretical perspective that the discontinuity effect flows from greater fear and greed in intergroup relative to interindividual interactions. Results reveal that each moderator shares a unique association with the magnitude of the discontinuity effect. The discontinuity effect is larger when (a) participants interact with an opponent whose behavior is unconstrained by the experimenter or constrained by the experimenter to be cooperative rather than constrained by the experimenter to be reciprocal, (b) group members make a group decision rather than individual decisions, (c) unconstrained communication between participants is present rather than absent, and (d) conflict of interest is severe rather than mild.     

Note on the squared multiple correlation as a lower bound to communality

A simple proof that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable is presented.     

Interpersonal attraction and person perception: Two tests of three balance models

Two experiments tested the adequacy of three balance models (equal-weights tetrahedron model, unequal-weights tetrahedron model, Feather model) for the p?o?x triad. In the first experiment, involving a variation of Byrne's anonymous-stranger technique, a PDP-11 computer was used to provide feedback on five attitude issues for each of the cells of a design created by five levels of the p?x variable (?2, ?1, 0, +1, +2) and five levels of the o?x variable (?2, ?1, 0, +1, +2). The dependent variable was p?o, interpersonal attraction. In the second experiment there were five-level manipulations of both p?x and o?p with an o-x (person perception) dependent variable. The correlations between obtained results and the predicted values for each of the three models were quite high (.64, .65, .61, respectively, in the first experiment and .60, .59, and .58, respectively, in the second), but the Feather model was judged least adequate. The data in the first experiment were best described by the unequal-weights tetrahedron model, and the data in the second experiment were best described by the equal-weights tetrahedron model. It was argued that avoidance of mutual dislike was responsible for the relatively greater support for the unequal-weights than equal-weights tetrahedron model in the first experiment.     

Popular induction: When is consensus information informative?1

An experiment was conducted in which information regarding a target persons evaluation of a target object was presented either in written form or via video tape, and information regarding the evaluations of four other people was also presented either in written form or via video tape. The results indicated that the effect of consensus on both person and object attribution was significantly weaker when the target-person information was video taped (concrete) and the other-people information was written (abstract) than in the other three conditions created by the combination of the two informational variables. It is argued that, in contrast to earlier speculation in the literature, type of consensus and its mode of presentation represent conceptually orthogonal dimensions. Further research is urged to map out the boundary conditions of consensus information; it is demonstrated that current work has largely concentrated upon only a portion of this attributional domain due to the prevalent confounding of these two independent dimensions.     

The use of mixed modeling to evaluate the impact of treatment integrity on learning

Treatment integrity, or the degree to which an intervention is implemented as intended, is a critical feature of skill acquisition tasks. Single‐case design consistently demonstrates that low treatment integrity slows or inhibits learning, but the relative impact of different types of instructional errors, or the presence of multiple errors, is less clear. The present study utilized a multilevel modeling approach to evaluate the impact of type of error (omission versus omission and commission) and error component (reinforcer delivery versus feedback) on learning. Findings revealed that learning outcomes worsened based on the type of error and as the complexity of errors increased; more specifically, participants performed better when only a single type of error occurred and when only a single error component was manipulated. Additionally, individual characteristics contributed to learning outcomes, highlighting the use of multilevel modeling as a helpful tool to supplement single‐case design. The differential impact of integrity errors on learning may be due to timing of errors (i.e., commission errors more likely to occur early in learning) or how errors affect reinforcement schedule versus discriminative control.